Synthesis of Networks

Up to now, we have considered flows or circulations only on a given network. But it is also quite interesting to study the reverse problem of designing a network (as economically as possible) on which a flow meeting given requirements can be realized. On the one hand, we will consider the case where all edges may be built with the same cost, and where we are looking for an undirected network with lower bounds on the maximal values of a flow between any two vertices. Both the analysis and design of such symmetric networks use so-called equivalent flow trees; this technique has an interesting application for the construction of certain communication networks which will be the topic of Section 12.4. On the other hand, we shall address the question of how one may increase the maximal value of the flow for a given flow network by increasing the capacities of some edges by the smallest possible amount.